WHO, WHAT, WHERE, and PI
Written By: Arman Momeni
I first recall learning about Pi in sixth grade; I was sitting in math class when our teacher moved beyond the scope of edges – squares and triangles – and began to discuss the never-ending circular world. At that age we were only concerned with perimeter and area, or in the case of a circle, circumference and area. Our teacher quickly taught us the formulas for a circle’s circumference and area, 2rPi and r^2Pi respectively. Instantly, dozens of hands rose, all asking the same question: What in god’s name is pi? However, our teacher prompted us to neglect such complex mathematical foundations and focus on the simple task at hand; “Pi is a button on your calculator” responded the teacher. However, I was filled to the brim with curiosity, eager to understand what this new symbol represented.
After a quick google search, I was confronted with the same anticlimactic answer across all the websites I clicked; Pi, approximately 3.14, is the ratio of the circumference of a circle to its diameter. My first reaction was filled with pure disappointment. I thought I had finally broken my way into advanced mathematics, but Pi was just as uninteresting as any other mathematical concept we had been taught. Nevertheless, something caught my eye in one of the articles I was reading. It simply stated that humans will never be able to find the exact value of Pi; now, I was intrigued. I pondered to myself: if Pi is a constant on my calculator, how is it possible that we don’t know its exact value? Upon further reading, I learned that, despite conventionally being rounded to 3.14, Pi pertains infinitely many digits, therefore, the value of Pi that we use on our calculator is only an approximation. After uncovering this new information, I was hooked, and wanted to learn more. This article by Science ReWired will tell you all about the intriguing, unbelievable, and mind-boggling infinite life of Pi.
The History of Pi:
Pi has been known for almost 4000 years, when it was discovered by ancient Babylonians around 1900 – 1680 BC. The ancient Babylonians took 3 times the square of a circle’s radius to calculate its area, which gave them a value of pi = 3. However, as their society progressed so did their approximations for Pi. In fact, one tablet shows an inscription where pi = 3.125, which is not far from a current rounded approximation for pi, 3.141.
Side Note: 4000 years is a significant amount of time. There are 1,460,000 days in a period of 4000 years; however, if you add 1,460,000 digits of pi to 3.14 you would be approximating its value. There are 2,102,400,000 seconds in a period of 4000 years, add 2,102,400,000 digits of pi to 3.14 and you would STILL be approximating its value!
The first calculation of pi was performed by Archimedes of Syracuse in 287-212 BC. Archimedes approximated the area of a circle through his use of the famous Pythagorean Theorem. He found the areas of two regular polygons, inscribed a circle within the polygons and was able to find a very close value to the area of a circle. Archimedes was able to prove that the value of pi lies between 3 1/7 and 3 10/71. Through the use of inscribed polygons mathematicians were eventually able to calculate the value of pi to 35 digits.
Progress slowed for a while, however, now, in modern times, mathematicians are able to use computers and a formula, derived by Indian mathematician Srinivasa Ramanujan, to calculate a more exact value for Pi. In present day, the value of pi continues to be unravelled and discovered all the way beyond its 50 trillionth digit. Mathematicians are eager to discover patterns within Pi and search for any repeating sequences.
The Importance of Pi:
While it seems basic on the surface level, the fact that such a constant exists is fascinating. Regardless of the size of a circle, if you were to divide its circumference by its diameter, the resulting value would always be 3.14159265358… or pi. Pi is one of the most important known numbers, as it helps humanity build a clearer picture of the universe. Pi also helped to inspire a new notion of angle measurements, which is called radian measure. Additionally, the discovery of Pi has helped with calculations towards many of the insights within the physical world. Pi is used in many calculations involving construction, quantum physics, music theory, medical procedures, air travel, space flight, and communications.
Works Cited:
A brief history of pi (π) | exploratorium. (n.d.). https://www.exploratorium.edu/pi/history-of-pi
Courses, T. G. (2020, April 28). Pi: The most important number in the universe?. Wondrium Daily. https://www.wondriumdaily.com/the-origins-of-pi/#:~:text=It%27s%20the%20ratio%20of%20the,little%20bit%20bigger%20than%20three.&text=The%20constant%20π%20helps%20us,a%20new%20unit%20of%20measurement.
Bogart, S. (1999, May 17). What is pi, and how did it originate?. Scientific American. https://www.scientificamerican.com/article/what-is-pi-and-how-did-it-originate/
